Young's modulus and volume porosity relationships for additive manufacturing applications

Recent advancements in additive manufacturing (or rapid prototyping) technologies allow the fabrication of end-use components with defined porous structures. For example, one area of particular interest is the potential to modify the flexibility (bending stiffness) of orthopedic implants through the use of engineered porosity (i.e., design and placement of pores) and subsequent fabrication of the implant using additive manufacturing processes. However, applications of engineered porosity require the ability to accurately predict mechanical properties from knowledge or characterization of the pore structure and the existence of robust equations characterizing the property-porosity relationships. As Young's modulus can be altered by variations in pore shape as well as pore distribution, numerous semi-analytical and theoretical relationships have been proposed to describe the dependence of mechanical properties on porosity. However, the utility and physical meaning of many of these relationships is often unclear as most theoretical models are based on some idealized physical microstructure, and the resulting correlations often cannot be applied to real materials and practical applications. This review summarizes the evolution and development of relationships for the effective Young's modulus of a porous material and concludes that verifiable equations yielding consistently reproducible results tied to specific pore structures do not yet exist. Further research is needed to develop and validate predictive equations for the effective Young's modulus over a volume porosity range of 20-50 %, the range of interest over which existing equations, whether based on effective medium theories or empirical results, demonstrate the largest disparity and offers the greatest opportunity for beneficial modification of bending stiffness in orthopedic applications using currently available additive manufacturing techniques.